Now that we have set-up an expressive approximation to \(c\) -concave functions we can take the same route as [1]}, and define individual flow
blocks \(s_j\) , \(j\in [T]\)  (see e:sascomp) using the exponential map as suggested by McCann's theorem.
Each flow block \(s_j\)  is defined as:
\(s_j(x)&=\exp (-\nabla _x\phi _j(x)), \quad j=1,\ldots , T\\\phi _j(x) &= \min _{i\in [m]} \left( c(x,y^{(j)}_i) + \alpha ^{(j)}_i\right).\) 
